Time and temperature dependent mechanical characterization of polymer‐based materials in electronic packaging applications

Abstract

The thermo‐mechanical testing of high performance polyimide films Type HPPST supplied by Dupont^® was conducted at different strain rates and in different temperature environments. The stress‐strain behavior of materials was investigated, and the dependence of Young's modulus on temperature and strain rate is reported. In view of the uncertainty of the Young's modulus determination, the specimens were tested with unloading‐reloading to verify the test results. Constant strain rate uniaxial tensile tests and long‐time creep tests at various temperatures were performed to characterize the time‐temperature‐dependent mechanical property precisely. Cyclic loading tests were also implemented on specimens to investigate cyclic stress‐strain behaviors. This research is expected to enhance finite‐element‐modeling accuracy and characterize material properties precisely.     

Uniaxial compression of SiO2 glass cylinders: Analysis using stress‐dependent material coefficients

The present publication extends the prior analysis and discussion of data from the uniaxial compression (upsetting) of hot glass cylinders of vitreous silica that clearly revealed nonlinearity in viscoelastic parameters, i. e., Young's modulus and viscosity. While the simple Maxwell model is retained, the assumption of constant material coefficients in the course of an experiment is dropped. Two approaches, supported by both numerical integration and FEM simulations are applied to unravel the stress dependence of Young's modulus and the viscosity. Thus, nonlinearities are manifested by a non‐Hookean elasticity and a non‐Newtonian viscosity. The stress relaxation behaviour has also been analyzed disregarding any particular model. The relaxation ability is characterized by thermorheological simplicity depending on both the temperature and the stress attained.     

Characterization of single crystal silicon and electroplated nickel films by uniaxial tensile test with in situ X-ray diffraction measurement

In this study, mechanical properties of micron‐thick single crystalline silicon (Si) and electroplated nickel (Ni) films at intermediate temperatures are investigated by means of X‐ray diffraction (XRD) tensile testing. The developed tensile test technique enables us to directly measure lateral (out‐of‐plane) elastic strain of microscale crystalline specimen using XRD during tensile loading, and determines Young's modulus, Poisson's ratio and tensile strength of the Si and Ni specimens. The specimens, measuring 10 μm thick, 300 μm wide and 3 mm long, are prepared through a conventional micro‐machining process, and the ultraviolet lithographie galvanoformung abformung (UV‐LIGA) process including a molding and an electroplating. The Si specimens, showing brittle fracture at room temperature (R.T.), have average Young's modulus and Poisson's ratio of 169 GPa and 0.35, respectively, in very good agreement with analytical values. The Ni specimens, showing ductile fracture, have those of 190 GPa and 0.24, lower than bulk coarse grained Ni. Young's moduli of both the Si and Ni specimens decrease with increasing temperature, but Poisson's ratios are independent of temperature. The influence of specimen size on elastic‐plastic properties of the specimens is discussed.     

Mechanical properties of metal and compound films

Experimental results on internal stress, Young's modulus and adhesion of metal and compound films are presented and the correlation between these quantities is discussed. Internal stress and Young's modulus were determined by simultaneous in situ measurements during film deposition. In addition to the internal stress values of metal films, which have been given by many workers, we include results on compound films, some of which showed compressive stresses. The Young's moduli of films of such compounds as MgF₂ and TiC and of carbon, which have not previously been established, were determined. The strain energy density accumulated in a film during deposition was evaluated from the measured values of Young's modulus and internal stress. In some films, cracks or wrinkles were generated by strain energy, leading to the spontaneous peeling of the films from the substrates. The adhesion experiments were performed using the topple and pull test. The adhesive forces were directly measured and the adhesion energies were estimated. The effect of the substrate temperature and ion bombardment on the adhesion were investigated. The values of adhesion energies were compared with strain energies and the meaning of the adhesion test was considered.     

Biomechanical properties of single chondrocytes and chondrons determined by micromanipulation and finite-element modelling

A chondrocyte and its surrounding pericellular matrix (PCM) are defined as a chondron. Single chondrocytes and chondrons isolated from bovine articular cartilage were compressed by micromanipulation between two parallel surfaces in order to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during compression to various deformations and then holding. When the nominal strain at the end of compression was 50 per cent, force relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant when the nominal strain was 30 per cent or lower. The viscoelastic behaviour might be due to the mechanical response of the cell cytoskeleton and/or nucleus at higher deformations. A finite-element analysis was applied to simulate the experimental force-displacement/time data and to obtain mechanical property parameters of the chondrocytes and chondrons. Because of the large strains in the cells, a nonlinear elastic model was used for simulations of compression to 30 per cent nominal strain and a nonlinear viscoelastic model for 50 per cent. The elastic model yielded a Young''s modulus of 14 ± 1 kPa (mean ± s.e.) for chondrocytes and 19 ± 2 kPa for chondrons, respectively. The viscoelastic model generated an instantaneous elastic modulus of 21 ± 3 and 27 ± 4 kPa, a long-term modulus of 9.3 ± 0.8 and 12 ± 1 kPa and an apparent viscosity of 2.8 ± 0.5 and 3.4 ± 0.6 kPa s for chondrocytes and chondrons, respectively. It was concluded that chondrons were generally stiffer and showed less viscoelastic behaviour than chondrocytes, and that the PCM significantly influenced the mechanical properties of the cells.     

Ultra‐High‐Speed Full‐Field Deformation Measurements on Concrete Spalling Specimens and Stiffness Identification with the Virtual Fields Method

Abstract: For one decade, spalling techniques based on the use of a metallic Hopkinson bar in contact with a concrete sample have been widely employed to characterise the dynamic tensile strength of concrete at strain rates ranging from a few tens to hundreds of s^?1. However, the processing method based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic. In particular, the identification of the whole softening behaviour of the concrete material is currently out of reach. In the present paper, a new processing technique is proposed based on the use of the virtual fields method (VFM). First, a digital ultra‐high‐speed camera is used to record the pictures of a grid bonded onto the specimen. Then, images of the grid recorded by the camera are processed to obtain full‐field axial displacement maps at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests with different impact parameters allowed the identification of Young's modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when microdamage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. It was then possible to construct local stress–strain curves and derive a tensile strength value.     

Experimental Investigation of Strain Behaviour of Heated Cement Paste and Concrete

The material degradation of concrete subjected to fire events has a severe influence on the load‐carrying capacity of support structures. Spalling of concrete layers, exposing the reinforcement bars and degradation of the material properties (Young's modulus, compressive strength) may lead to significant damage of the reduced cross‐section and, therefore, cause failure of the structure. In order to understand the stress build‐up at the heated surface caused by thermal expansion due to fire loading, finally leading to damage and spalling of concrete, the strain behaviour of cement paste and concrete exposed to combined thermo‐mechanical loading is the focus of this work. Hereby, the evolution of thermal strains, Young's modulus and Poisson's ratio with increasing temperature are investigated experimentally. For this purpose, the specimens are loaded uniaxially while the temperature is increased up to 800 °C. The obtained results provide the proper basis for the development of realistic material models, allowing more sophisticated simulations of structures exposed to fire.     

Mechanical characterization of single crystal silicon and UV-LIGA nickel thin films using tensile tester operated in AFM

This paper describes the mechanical characteristics of microscale single crystal silicon (SCS) and UV‐LIGA nickel (Ni) films used for microelectromechanical systems (MEMS). A compact tensile tester, operated in an atomic force microscope (AFM), was developed for accurate evaluation of Young's modulus, tensile strain and tensile strength of microscale SCS and UV‐LIGA Ni specimens. SCS specimens with nominal dimensions of 20 μm in thickness, 50 μm in width and 600 μm in length were prepared by a conventional photolithography and etching process. UV‐LIGA Ni specimens, with a thickness of 15 μm, a width of 50 μm and a length of 600 μm in nominal dimensions, were also fabricated by electroplating using a UV thick photoresist mould. All specimens have line patterns on their specimen gauge section to measure axial elongation under tensile loading. The SCS specimens showed a linear stress–strain response and fractured in a brittle manner, whereas the UV‐LIGA Ni specimens showed elastic–inelastic deformation behaviour. Young's modulus of SCS and UV‐LIGA Ni specimens obtained from tensile tests averaged 169.2 GPa and 183.6 GPa, respectively, close to those of bulk materials. However, the tensile strength of both materials showed a larger value than the bulk materials: 1.47 GPa for the SCS and 0.98 GPa for the Ni specimens. Yield stress and breaking elongation of UV‐LIGA Ni specimens were also quite different from those of the bulk Ni because of the specimen size effect on inelastic properties.     

Young's modulus of electroplated Ni thin film for MEMS applications

The Young's modulus of an electroplated nickel (Ni) thin film suitable for microelectromechanical applications has been investigated as a function of process variables: the plating temperature and current density. It was found that the Young's modulus is approximately 205 GPa at plating temperatures less than 60 °C, close to that of bulk Ni, but drastically drops to approximately 100 GPa at 80 °C. The inclusion of ammonium and sulphate ions by hydrolysis is believed to be responsible for the sharp drop. The Young's modulus of 205 GPa is for a Ni film plated at J=2 mA/cm² and it decreases to 85 GPa as the plating current density is increased to 30 mA/cm². The results imply that at low current density, the plating speed is slow and there is sufficient time for the as-plated Ni atoms to rearrange to form a dense coating. At high currents, the plating speed is high, and the limited mass transport of Ni ions leads to a less dense coating.     

Static and dynamic mechanical properties of poly(vinyl chloride) loaded with aluminum oxide nanopowder

A series of nanocomposites from poly(vinyl chloride) loaded with different concentrations of Al₂O₃ nanopowder was prepared. The tensile mechanical properties of these composites were studied at different temperatures namely; stress–strain curves. The elastic modulus was calculated and found to decrease with increasing both filler loading and temperature. The strain at a certain stress at different temperatures was studied and the thermal activation energy for polymer chains was calculated. The complex viscosity as well as the storage modulus was found to decrease with increasing the filler loadings at different frequencies. The relaxation time of the polymer matrix was calculated and found to independent on the concentration of the filler but it decreased linearly with increasing frequency. The glass transition temperature was found to increase with increasing both filler loading and frequency.     

Plasticity improvement for dendrite/metallic glass matrix composites by pre-deformation

The mechanical properties of in-situ metallic glass matrix composites (MGMCs) are investigated by tensile pre-deformation, followed by compression. The pre-deformation is utilized to exploit notable increases in plasticity, accompanied by slight increases in the compressive strength, and the deformation mechanisms are explored. The increased free volumes in the glass matrix after tensile pre-deformation contribute to the decrease of the Young's modulus of the glass matrix and lead to the increase in the stress concentration, promoting multiplication of shear bands. When the Young's modulus of the glass matrix matches that of the dendrites, the plasticity of in-situ dendrite-reinforced MGMCs is the optimized. Matching Young's modulus opens a door to design the MGMCs with excellent plasticity and remarkable work-hardening capability.     

Effect of simple stress on the glass transition of polymers at high pressures

Experimental studies, which have been carried out in this laboratory, showed the yield strength in tension, compression, and shear in the rubbery and the glassy states increased with increasing hydrostatic pressure. Moreover, the Young's modulus also increased with pressure and the amount of the increase across the glass transition temperature (T _g) at a given pressure can be as large as three orders of magnitude in the case of elastomers. An extension of the Gibbs-Dimarzio theory is proposed to account for the effect of applied stress on the glass transition temeprature of glass-forming polymers. When a simple stress, such as tensile, compressive or shear stress, is applied to a polymer, the T _g will decrease, compared to a polymer without applied stress. A glass-forming polymer in the vicinity of the transition would behave differently from that predicted by rubber elasticity. The partition function taking into account the effect of stress is suggested to be $$\Gamma = \Sigma W(f, n_0 ){\text{ }}\exp {\text{ }}[ - \beta (PV + U - \sigma V\varepsilon )]$$ where the strain ?=σ (f ? f ₀) in which f and f ₀ are the fraction of flexed bonds with and without stress, respectively. Furthermore, by this model, the Young's modulus across the transition, E _L and E _G, can be evaluated. The Young's modulus increases with increasing pressure at lower and moderate pressure range but the increase is rather small at very high pressure range.     

The stiffness of unidirectionally reinforced CFRP as a function of strain rate,strain magnitude and temperature

The Young's modulus and shear modulus of a unidirectional carbon fibre-reinforced plastic composite were measured at −40°C, 20°C, 80°C and 120°C over the strain range 0–0.9%. Within the strain range 0.1%–0.9%, a non-linear increase of up to 20% was found in the Young's modulus, which was independent of strain rate. The shear modulus was sensitive to the viscoelastic properties of the matrix; its magnitude decreased with increasing temperature and increased with increasing strain rate. However, this latter change was not very apparent, particularly at strains beyond 0.6%.     

Ultrastiff,Strong, and Highly Thermally Conductive Crystalline Graphitic Films with Mixed Stacking Order

A macroscopic film (2.5 cm × 2.5 cm) made by layer‐by‐layer assembly of 100 single‐layer polycrystalline graphene films is reported. The graphene layers are transferred and stacked one by one using a wet process that leads to layer defects and interstitial contamination. Heat‐treatment of the sample up to 2800 °C results in the removal of interstitial contaminants and the healing of graphene layer defects. The resulting stacked graphene sample is a freestanding film with near‐perfect in‐plane crystallinity but a mixed stacking order through the thickness, which separates it from all existing carbon materials. Macroscale tensile tests yields maximum values of 62 GPa for the Young's modulus and 0.70 GPa for the fracture strength, significantly higher than has been reported for any other macroscale carbon films; microscale tensile tests yield maximum values of 290 GPa for the Young's modulus and 5.8 GPa for the fracture strength. The measured in‐plane thermal conductivity is exceptionally high, 2292 ± 159 W m^?1 K^?1 while in‐plane electrical conductivity is 2.2 × 10⁵ S m^?1. The high performance of these films is attributed to the combination of the high in‐plane crystalline order and unique stacking configuration through the thickness.     

Effect of hydrogen on the Young's modulus of commercial purity iron

• 1.1. The apparent Young's modulus and elastic strain of commercial purity iron increased by 0.11% and 12.9%, respectively, during aging after severe charging.
• 2.2. The increase of apparent Young's modulus of commercial purity iron during aging after charging was nearly equal to that after artificial partial stress relaxation. That is to say, hydrogen does not significantly change the Young's modulus associated with the interatomic cohesive force of commercial purity iron, even during aging after severe charging.

     

Some Physical Properties of Pure and Doped Polyvinyl Alcohol under Applied Stress

Thick films of polyvinyl alcohol (PVA) containing very finemetallic powder, copper (Cu), iron (Fe) and aluminum (Al) 2.5% by weight,were prepared by the casting method. The temperature dependence of Young'smodulus at constant stress, the stress dependence of Young's modulus(Y), the stress dependence of dielectric constant (ε) and stressdependence of phonon velocity, were studied. It was found that Young'smodulus (Y) of the pure sample has the lowest value and that of PVA + Alhas the highest value. This can be explained on the basis that Ydepends on the ratio between the energy of molecular interactions andthe energy of thermal motion of the sample units. We also found that thedielectric constant increases with the addition of metallic powder, andwith an increasing applied stress. The phonon velocity increased withincreasing stress. The increase of stress decreases imperfectionsleading to the increased phonon velocity. The electronic absorptionspectra of PVA is not affected by doping Al and Fe, whereas the PVA dopedwith Cu shows a shift of the absorption maxima toward a longer wavelength.The instantaneous elastic behavior may be observed only at lowtemperatures and very short creep times.     

Structural investigations of thermotropic hydroxypropylcellulose

Abstract

The tensile properties of hydroxypropylcellulose sheets which were formed by means of hot compression at temperatures between 150° and 220°C were examined at room temperature. The marked increase of elongation at breaking and the decrease of the Young's modulus over temperatures of 210°C agreed well with the phase transition observed by the polarized light microscope. These phenomena have been explained by X‐ray and SEM studies.     

Non-linear elastic behaviour of flexible fibre composites

An elastic constitutive model is developed for flexible fibre composites which are composed of continuous curved fibres and ductile matrices. The prediction of non-linear stress/strain responses of the composites is performed by a stepwise incremental analysis. Numerical results of the uniaxial tensile stress/strain relations are obtained for several types of composites, containing glass or Kevlar fibres in an elastomeric polymer. Unique properties of the flexible composites are: (1) low Young's modulus in the range of low applied stress and high modulus in the range of high applied stress; (2) enhanced elongation; and (3) high energy associated with deformation.     

Effect of dynamic strain aging on fatigue crack growth behaviour of reactor pressure vessel steels

Abstract

Fatigue tests under constant amplitude load were conducted on compact tension specimens of SA533B3 steels with four levels of sulphur content at different temperatures. A modified capacitance type crack opening displacement (COD) gauge was shown to be suitable for fatigue crack length measurement at high temperatures. Test results obtained with different measurement techniques show good consistency. The observation that the Young's moduli measured at a strain rate of 4 × 10^?3 s^?1 for the SA533B3 steels at 150 and 300°C do not decrease with increasing temperature seems to be related to the presence of dynamic strain aging. The fatigue crack growth rates at 150 and 300°C are about two and half times slower than those tested at 400°C because dynamic strain aging prevails at 150 and 300°C. Fractographic examination results suggest that inclusions embedded in secondary cracks enhanced the fatigue crack initiation rather than the fatigue crack growth.     

Mechanical characterization of free-standing polypyrrole film

Free-standing polypyrrole films, neutral or doped with ClO₄⁻, have been mechanically characterized. Their elasticity of both dry and wet states was characterized by mean of the Young's modulus. In addition, the Young's modulus was calculated as a function of the film oxidation deep by “in situ” polarization at different potentials ranging from − 0.6 up to 0.8 V. The samples also were characterized under oxidation and reduction by reverse constant currents. When the films were submitted to a constant stretching force the length variations were obtained. At a constant length of the sample the electro-chemo-mechanical force developed by the redox processes was obtained. As predicted by the ESCR model lineal variations of both, length and force, as a function of the consumed charge were obtained.